[no subject]

[Logical Language Group <lojbab@GREBYN.COM>]

OK.  Had a nice chat with pc tonight, and am either now very clear or
very confused.  I'll let you people tell me which.  As usual, in writing
this up, I am extrapolating from what pc said, partly because I didn't
use a tape recorder, and partly because I need to understand the
concepts myself, and not just quote him.  So if this is garbage, it may
be pc's error, my error or a communications gap between us.

The subject is our old friends individuals, sets, and masses.  While I
wanted to run the results of the discussion of "mei" past him, the
immediate question of the day was what the proper place structure should
be for "girzu".  How does a group differ from a set, a mass, and any
other thing that one might try to compare it with?

pc says that first and foremost, EVERYTHING that is a sumti is a set - a
mathematical set, to be clear.  A set is comprised of some members which
share some common property (which may merely be that of being members of
the set). cmima is the gismu that deals with sets and members. x1 is one
or more members of the set, x2 is the set as a whole, which may be
defined either in terms of the common property(ies) (using
"lo'i/le'i/la'i", or as some form of complete explication of the
membership, (member ce member ...), or as a conversion of one of the
other kinds of sumti, which according to pc is merely bringing out for
inspection the set that underlies that other sumti.

(Note that cmima does not have the common property as part of its place
structure.  This is because it is used to talk about the specific
relation of one or more members to the whole. kampu is used to talk
about the common property(ies)).

When we use a sumti that is not explicitly a set, we are taking that set
and looking at it in some different way:  as individuals, as an
aggregate, a mass, a team - there are a lot of words that can be used
and each of them has its own nuances of meaning.  When you look at a set
in such a different way, you can then talk about the properties that the
set holds when looked at that way.  This differs depending on the aspect
you are talking about.

One way to talk about a set is in terms of its individuals, and this is
what we are normally doing with "le", Ek(logically)-connected sumti,
etc.  You haven't got anything more than a set here - just the members,
and you may be talking here about the common property that they hold.

Let us turn to masses.  A mass is a set.  But it is a set that you look
at NOT in terms of the properties that the members exhibit separately,
but in terms of the properties that the members exhibit as a whole,
AMORPHOUSLY.  We do not care about the interrelationships among the
members that lead to these mass properties, but only about the mass
amorphous properties.  Indeed, once we have massified the set, when we
talk about the mass in terms of these properties, we no longer care
about the individual members.  Instead we can talk about amorphous
pieces/portions of the mass.  A piece of a mass is some portion of the
whole that exhibits all of the >relevant< properties of the whole.  A
quantum (kantu) is then the smallest piece that exhibits some mass
property.  It is meaningless to talk about pieces of the mass
independent of the mass properties.  The mass of Lojban List subscribers
incorporates me, and therefore my left thumb, but there are few mass
properties of the mass of Lojban List subscribers for which my thumb can
truly be said to be a "piece" of the mass.  Similarly, a molecule of
water does not exhibit many properties of the mass of water - it is
rather hard to say whether a single molecule is a solid, a liquid, or a
gas, for example, in terms of exhibiting the properties of solid, liquid
and gaseous water respectively.

Let us now turn to "system" (ciste).  A system consists of a set of
elements.  This set of elements is not really interesting in terms of
any properties of the individual elements (hence is a little like a
mass).  Indeed the membership of the system is not interesting.  But a
system has something else that is important.  It has a structure such
that the interrelationships between elements is defined.  Those
interrelationships give rise to properties (looks like a mass so far).
However because we have focussed on these properties as deriving from
interrelationships, the system is not amorphous like a mass.  (It may be
true that all "mass" properties are as a result of systemic
interrelationships among the components, but in a mass we are focussed
on the properties, and ignoring the interrelationships that bring them
about.)  The system is defined in terms of the interrelationships, and
the properties that result (and maybe even the members that are
incorporated) are secondary to these interrelationships - the structure
of the system.  Indeed the elements of a system are exactly those which
have an interrelationship with other elements.

Finally we come to "group" (girzu) which fills a spot somewhere in the
middle between total focus on the interrelationships and structure
(system), and properties of the whole (mass) and properties of
individuals (sets).  A group has all of these, and ALL of them are more
or less important.  Thus the place structure for girzu is something like
x1 is a group exhibiting group properties x2, composed of membership x3
(set) linked by interrelationships/group structure x4.  (note that x3
may defined as a membership or in terms of common properties of the
membership as individuals - this is true of all place structure
references to "set").  Some implications of this place structure are
that it is clear that the same membership can form a variety of
unrelated groups.  A set of 5 people can form many groups, for example 5
different groups with 5 different people as president, each organized
for a different function.  Same membership, possibly even focussed on
the same properties that the five hold in common, but having 5 different
sets of interactions and hence 5 different "group" manifestations.
These groups may in turn have nothing in common other than that
membership.

pc noted that this definition has a kinship with that of mathematical
group.  A mathematical group has an operation which defines the
interaction among the members of the group, and identity and inverse
elements that define properties that the group reveals as a whole (as
well as further interactions among members of the group).

Some examples, all extrapolations from the above:

A bunch of grapes or bananas is a group, because they are joined
together by a fixed structure with each grape in a relationship to each
other grape, in this case one of physical attachment.  But when we eat
"grapes" we are eating "of the mass of grapes" because it isn't clear
that the properties relevant to our eating have anything to do with the
structure of the bunch that we ate.

A baseball team may be thought of as a group, since the internal
structure is significant.  But when you look at the win-loss column
without caring about the individual players or their roles, you are
considering that team as an amorphous mass.  Wins and losses are mass
properties of the team; the batting order for tonight's game is a group
property.

A "sequence" (porsi) is defined in terms of its members, like simple
sets, and in terms of a specific group of interrelationships, like a
system.  But there are no "system" properties distinct from the
individual properties.  So most sequences are not groups or systems.

The terms for the smaller subunits should be apportionable among these.
"Elements" are the general term for the smallest pieces of sets and
systems and sequences, but seems inappropriate for "groups" (I'm not
sure why).  "quantum" and "portion" seems limited to masses, being the
smallest "piece" and any "piece" less than the whole which sdisplays the
common property, respectively.  "Members" go with systems and groups and
sets.  "Parts" and "components" seem limited to sequences, sets, and
groups since the terms seem clearly tied to their relationship with the
whole.

We have many more terms than we have descriptors, but this is not really
a problem. lo/le/la focus on the properties of the individuals.
loi/lei/lai focus on the properties of the group. lo'i/le'i/la'i focus
on the properties of the set.  Each of these then effects a 2-place
relationship.
description property<->individuals fitting that description individually,
description <-> mass exhibiting that decription property collectively
description<->mathematical set comprised of those individuals meeting that
    description individually.

Structure never plays a part in these two place relationships, and
probably could not without expanding the grammatical relationship to at
least 3 parts (members, relationship, and resulting properties).

The non-logical connectives fill in some of the gaps, but are also
essentially two-dimensional.  Only the "respectively" operator, which is
the most difficult to use, exhibits a third dimension, and then only by
being used in parallel in multiple sumti.

Thus sumti description is confined to two dimensional slices of
sometimes more complex wholes.  You can use mass descriptions to talk
about the common properties of systems and groups, but you get no
indication of the substructures that comprise them which in turn may
limit the degree to which portions of the system or group can display
relevant traits of the whole.  The mass "Internet" ("lai mela Internet")
is relatively meaningless without the backbone that ties it together,
which each of us connected to the net has some relationship with or you
wouldn't be reading this.  Though we know that Internet is a system, but
we can talk about its mass properties in a description, forgetting for
purposes of reference that the structure taht defines the net even
exists.

A side-implication of considering all sumti as some way of looking at a
set is that some non-logical connectives gain meaning when used to join
non-set sumti.  We actually realized this during our local group session
this evening (before I talked to pc) in trying to sort out all these
miscellaneous assortments of things.  For example, we can talk about
union and intersection in terms of Venn diagrams which are
REPRESENTATIONS of sets rather than sets themselves.  Specifically,
intersection applied to non-sets, has the approximate keyword "overlap"
(which has only slightly different meanings when you talk about masses
vs. individuals of a set).  I can't think of a good keyword for "union"
since the whole may be less than the sum of its parts, so I'll stick
with "union" and let people picture the Venn diagram.

Some non-malglico lujvo for these two terms would be useful.

In light of this discussion, the place structure of #mei should be
re-examined. x1 could be a mass, a group, a system, a team under this
discussion - the essence is some GROUP property, and this position will
normally be filled by a reference to that group property.  The
mathematical set - the membership as a whole - is x2, and that fits a
discussion of an n-some or n-tuple. x2 would be filled either by a list
of members or by a reference using le'i and friends to the property that
the INDIVIDUALS hold in common.  It is not clear what x3 has to do with
this - it is biased towards the set perspective by looking at
individuals but only as individuals, and masses don't care about them.
But it gives nothing about components of the masses, interrelationships
among groups and systems, etc. all of which otherwise fit the first two
places.  I think that the x3 place does no harm as long as we aren't
playing around with the empty set nomei (and I won't pretend to know
what that implies), but I'm not sure it is useful and/or metaphysically
necessary in most situations where "mei" is applicable.  I would err on
the side of metaphysical parsimony, but will not object if John and
Colin still want it.

Here are place structures for the words talked about in this message as
they stand right now:

cmima

x1 is a member/element of set x2; x1 belongs to group x2; x1 is
amid/among/amongst group x2 [x1 may be a complete or incomplete list of
members; x2 is normally marked by la'i/le'i/lo'i, defining the set in
terms of its common property(ies), though it may be a complete
enumeration of the membership]; (cf. ciste, porsi, jbini, girzu, gunma,
klesi, cmavo list mei)

ciste

x1 (mass) system interrelated by structure x2 among components x3 (set)
displaying x4 (ka) [x1 (or x3) is synergistic in x4; also network; x2 also
relations, rules; x3 also elements; x4 systemic functions/properties]
(cf. cmavo list ci'e, cmima, girzu, gunma, stura, tadji, munje)


gunma

x1 is a mass/team/aggregate/whole, together composed of components x2,
considered jointly [A description in x1 indicates of mass property(ies)
displayed by the mass; masses may reveal properties not found in the
individual set members that are massified, which themselves are not
necessarily relevant to the mass property implicit in this bridi]; (cf.
bende, girzu, pagbu)

kantu

x1 is a quantum/ray/elementary particle/smallest measurable increment of
property/activity x2 [ray (= wave-quantum)]; (cf. selci for masses and
most objects; ratni, gradu)


girzu

x1 is group/cluster/team showing common property (ka) x2 due to set x3
linked by relations x4 [also collection, team, comprised of, comprising;
members x3 (a specification of the complete membership) comprise group
x1]; (cf. bende, ciste, cmima, gunma)

bende

x1 is a crew/team/gang/squad/band of persons x2 directed/led by x3
organized for purpose x4 (x1 is a mass; x2 is a set); [also orchestra,
outfit; x3 conductor]; (cf. gunma, girzu, dansu, jatna, jitro, minde,
ralju)


mei

convert number to cardinality selbri; x1 is the mass formed from set x2
whose n member(s) are x3 [x1 is a mass with N components x3 composing
set x2; x2 is an n-tuple; x1 forms an n-some]; (cf. cmima, gunma, cmavo
list moi)

kampu

x1 (property - ka) is common/general/universal among members of set x2
(cf. cafne, rirci, fadni, cnano, tcaci, lakne, cmima)

lojbab